Stats 250 Full RLabs for Fall 2015

101 Pages·2015·8.92 MB·English

Author: Brenda Gunderson, Ph.D., 2015

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Statistics
 250

Lab
 Workbook

Fall
 2015

Weekly
 Labs
 and
 Supplements

Used
 in
 all
 lab
 sections
 of
 Stat
 250

Dr.
 Brenda
 Gunderson

Department
 of
 Statistics

University
 of
 Michigan

Table
 of
 Contents

Material
  Page

Note
 to
 Students
 and
 Supplements
  1

  Supplement
 1:
 R
 Commands
 Summary
  2

  Supplement
 2:
 Notation
 Sheet
  4

  Supplement
 3:
 Name
 That
 Scenario
  6

  Supplement
 4:
 Interpretation
 Examples
  8

  Supplement
 5:
 Summary
 of
 the
 Main
 t-­‐Tests
  10

  Supplement
 6:
 Regression
 Output
 in
 R
  12

Lab
 1:

 Describing
 Data
 with
 Graphs
 and
 Numbers
  15

Lab
 2:

 Probability
 and
 Random
 Variables
  19

Lab
 3:

 Confidence
 Intervals
 for
 a
 Population
 Proportion
  27

Lab
 4:

 Hypothesis
 Testing
 for
 a
 Population
 Proportion
  33

Lab
 5:

 Understanding
 Normal
 and
 Random
 Data
  39

Lab
 6:

 Learning
 about
 a
 Population
 Mean
  47

Lab
 7:

 Paired
 Data
 Analysis
  53

Lab
 8:
  Comparing
 Two
 Means
  59

Lab
 9:
  One-­‐Way
 Analysis
 of
 Variance
 (ANOVA)
  67

Lab
 10:Exploring
 Linear
 Regression
  75

Lab
 11:
 Regression
 Inference
  81

Lab
 12:
 Chi-­‐Square
 Tests
  85

Note
 to
 Students

Welcome
 to
 Statistics
 250
 at
 the
 University
 of
 Michigan!

This
 is
 the
 first
 summer
 term
 in
 which
 R
 and
 R
 Commander
 will
 be
 used
 as
 the
 software
 package
 for

Stats
 250.

 Some
 of
 the
 reasons
 why
 we
 made
 this
 switch
 are:

• The
 ability
 to
 use
 R
 is
 a
 valuable
 skill
 recognized
 by
 employers.

• Other
 Statistics
 courses
 use
 R
 and
 this
 will
 make
 for
 an
 easier
 transition
 into
 these
 next
 courses.

• R
 is
 a
 free,
 open
 source
 software
 that
 can
 be
 downloaded
 onto
 student
 machines,
 so
 students

can
 have
 access
 to
 it
 any
 time
 on
 their
 personal
 devices
 and
 won't
 have
 to
 use
 Virtual
 Sites.

This
 lab
 workbook
 is
 designed
 for
 you
 to
 use
 in
 lab
 and
 as
 extra
 preparation
 for
 exams.

 In
 the
 workbook,

you
 will
 find
 the
 following
 materials:

Supplemental
 Material
 –
 great
 summaries
 for
 reference
 throughout
 the
 term:

1.
  R
 Commands
 Reference

2.
  Notation
 Sheet

3.
  Name
 That
 Scenario

4.
  Interpretation
 Examples

5.
  Summary
 of
 T-­‐tests

6.
  Regression
 Output
 in
 R

Weekly
 Labs
 (numbered
 1
 to
 12)
 –
 each
 lab
 contains
 the
 follow
 parts:

o Lab
 Background
 –
 objective
 and
 brief
 overview
 material,
 which
 is
 good
 to
 take
 a
 couple
 minutes
 to

read
 before
 you
 come
 to
 lab
 each
 week.

o Warm-­‐Up
 Activity
 –
 quick
 questions
 for
 you
 to
 do
 before
 the
 In-­‐Lab
 Project,
 usually
 a
 quick
 review
 of

concepts
 you
 have
 seen
 in
 lecture.

o ILP
 (In-­‐Lab
 Project)
 –
 one
 or
 more
 activities
 you
 will
 work
 on
 in
 lab,
 in
 groups.

o Cool-­‐Down
 Activity
 –questions
 for
 you
 to
 do
 after
 the
 ILP
 for
 further
 reflection
 and
 application
 of

the
 concepts
 covered
 in
 the
 ILP.

The
 Labs
 are
 designed
 to
 be
 interactive
 and
 to
 provide
 you
 with
 a
 complete
 example
 for
 each
 concept.

Completing
 the
 corresponding
 PreLab
 assignment
 (a
 link
 to
 video
 instructions
 for
 PreLabs
 will
 be
 on

Canvas
 and
 the
 Stat
 250
 YouTube
 channel)
 and
 reading
 the
 upcoming
 lab
 background
 overview
 before

lab
 each
 week
 is
 a
 good
 way
 to
 prepare
 for
 the
 various
 lab
 activities.

Good
 luck
 in
 Statistics
 250!

-­‐-­‐
 The
 Stat
 250
 Instructors
 and
 GSIs

Special
 Thanks
 to
 the
 Statistics
 Graduate
 Students

Kit
 Clement

Sean
 Pikosz

Daniel
 Walter

For
 their
 substantial
 contributions
 to
 transition
 and
 modernize

the
 Lab
 Materials
 to
 the
 Awesome
 R
 computing
 package

1
Supplement
 1:
 R
 Commands
 Summary

By
 Lab
 –
 For
 Quick
 Reference

Lab
 1
 –
 Bar
 Charts,
 Histograms,
 Numerical
 Summaries,
 Boxplots

Open
 a
 data
 file
 after
 loading
 R
 Commander:
 Data
 >
 Load
 data
 set

To
 produce
 a
 Histogram:
 Graphs
 >
 Histogram

To
 generate
 Descriptive
 Statistics:
 Statistics
 >
 Summaries
 >
 Numerical
 summaries

To
 produce
 a
 Bar
 Chart:
 Graphs
 >
 Bar
 Graph

To
 produce
 a
 Boxplot:
 Graphs
 >
 Boxplot

Lab
 5
 –
 Time
 Plots,
 QQ
 Plots

To
 produce
 a
 Sequence
 or
 Time
 Plot
 for
 the
 variable
 named
 “VARIABLE”
 in
 the
 data
 set
 “DATA”

you
 must
 type
 these
 two
 lines
 of
 code
 into
 the
 R
 Script
 box:
plot(DATA$VARIABLE, type =”l”, main="Normal QQ Plot of variable
by name")

Note
 that
 you
 can
 find
 the
 dataset
 name
 in
 blue
 text
 at
 the
 top.
 To
 find
 variable
 names,
 click
 View
 data

set
 and
 look
 at
 the
 top
 row.
 To
 create
 the
 plot,
 highlight
 the
 above
 code
 and
 click
 the
 Submit
 button.

To
 produce
 a
 QQ
 Plot:
 you
 can
 use
 the
 built
 in
 option
 under
 Graphs
 >
 Quantile-­‐comparison
 plot

Or
 you
 can
 make
 a
 QQ
 plot
 for
 the
 variable
 “VARIABLE”
 in
 the
 data
 set
 “DATA”
 by
 typing
 these
 two
 lines

of
 code
 into
 the
 R
 Script
 box:

qqnorm(DATA$VARIABLE, main="Normal QQ Plot of variable by
name")
qqline(DATA$VARIABLE)

Then
 highlight
 this
 code
 and
 click
 the
 Submit
 button.

Lab
 6
 –
 One-­‐Sample
 t
 Procedures
 for
 a
 Population
 Mean

To
 perform
 a
 One-­‐Sample
 T
 Test
 for
 a
 population
 mean
 and
 obtain
 a
 confidence
 interval:
 Statistics
 >

Means
 >
 Single-­‐sample
 t-­‐test

Lab
 7
 –
 Paired
 t
 Procedures

To
 perform
 a
 Paired
 T
 Test
 and
 obtain
 a
 confidence
 interval:
 Statistics
 >
 Means
 >
 Paired
 t-­‐test

To
 compute
 Differences:
 Data
 >
 Manage
 variables
 in
 active
 data
 set
 >
 Compute
 new
 variable.

Lab
 8
 –
 Independent
 Samples
 t
 Procedures

To
 perform
 Levene’s
 Test:
 Statistics
 >
 Variances
 >
 Levene’s
 Test

2
To
 perform
 a
 Two-­‐Samples
 T
 Test
 and
 obtain
 a
 confidence
 interval:
 Statistics
 >
 Means
 >
 Independent

samples
 t-­‐test

Lab
 9
 –
 One-­‐way
 Analysis
 of
 Variance
 (ANOVA)

To
 perform
 an
 ANOVA:
 Statistics
 >
 Means
 >
 One-­‐Way
 ANOVA

Lab
 10
 and
 11
 –
 Linear
 Regression

To
 produce
 the
 correlation
 (R)
 for
 all
 pairs
 of
 variables:
 Statistics
 >
 Summaries
 >
 Correlation
 matrix

To
 produce
 a
 Scatterplot:
 Graphs
 >
 Scatterplot

To
 perform
 a
 Linear
 Regression:
 Statistics
 >
 Fit
 models
 >
 Linear
 regression

To
 produce
 a
 Residual
 plot
 and
 QQ
 Plot
 of
 residuals,
 first
 make
 sure
 you
 have
 the
 correct
 model

selected,
 then
 follow:
 Models
 >
 Graphs
 >
 Basic
 diagnostic
 plots

Lab
 12
 –
 Chi-­‐Square
 Tests

To
 perform
 a
 Goodness
 of
 Fit
 Test:
 Statistics
 >
 Summaries
 >
 Frequency
 distributions.

 Make
 sure
 to

check
 the
 box
 to
 run
 a
 goodness
 of
 fit
 test,
 and
 then
 you
 can
 specify
 the
 null
 probabilities.

To
 perform
 a
 Test
 of
 Independence:
 Statistics
 >
 Contingency
 tables
 >
 Two-­‐way
 table

To
 perform
 a
 Test
 of
 Homogeneity:
 Statistics
 >
 Contingency
 tables
 >
 Two-­‐way
 table

3
Supplement
 2:
 Notation
 Sheet

The
 table
 below
 defines
 important
 notations,
 including
 that
 used
 by
 R,
 which
 you
 will
 come
 across
 in
 the

course.

 This
 is
 not
 an
 exhaustive
 list,
 but
 it
 is
 a
 fairly
 comprehensive
 overview
 of
 the
 “strange
 letters”

used
 in
 the
 course.

Note:
 Blank
 cells
 mean
 there
 is
 no
 corresponding
 notation.

Notation
 used
 in
 R

Name
  Population
 Notation
  Sample
 Notation

Commander

Summary
 Measures

Mean
  μ
 (read
 as
 “mu”)
  x
 (x-­‐bar)
  Mean

Proportion
  p
  pˆ (p-­‐hat)

Standard
 deviation
  σ
 (sigma)
  s
  Varies,
 often
 “sd”

Variance
  σ2
  s2
  Variance

Sample
 size

  n
  n
 (sometimes
 N)

Confidence
 Intervals

  z*
 (z-­‐star)

Multipliers

  t*
 (t-­‐star)

Margin
 of
 error

  m,
 m.e.

Hypothesis
 Testing

  z

  t
  t

Test
 statistics

Note:
 t,
 F,
 and
 χ2
 statistics

  F
  F

have
 degrees
 of
 freedom

(abbreviated
 df)
 associated

with
 them.

 Look
 for
 these

  χ2
 (chi-­‐square)
  Chi-­‐square

on
 your
 Formula
 Card.

Significance
 level

  α(alpha)

Pr(*)

p-­‐value

  p-­‐value
  (the
 star
 will
 depend
 on

what
 test
 is
 being
 used)

4
Name
  Population
 Notation
  Sample
 Notation
  Notation
 used
 in
 R

Analysis
 of
 Variance
 (abbreviated
 ANOVA)

Row
 labeled
 with
 the

Sum
 of
 squares
 for

  SSG
  grouping
 variable,

groups

column
 labeled
 Sum
 Sq

Sum
 of
 squares
 for
  Row
 labeled
 Residuals,

  SSE

error
  column
 labeled
 Sum
 Sq

Row
 labeled
 with
 the

Mean
 square
 for
  grouping
 variable,

  MSG

groups
  column
 labeled
 Mean

Sq

Row
 labeled
 Residuals,

Mean
 square
 error

  MSE
  column
 labeled
 Mean

Sq

Regression

Response
 (dependent)
  (given
 by
 name
 of
 y-­‐
y
  y

variable
  variable)

Predicted
 (estimated)
  E(y)
 (expected
 value
 of

yˆ (y-­‐hat)

response
  y)

Explanatory
  (given
 by
 name
 of
 x-­‐
x
  x

(independent)
 variable
  variable)

B
 (look
 in
 the
 row

y-­‐intercept
  β
 (beta-­‐not)
  b

o o labeled
 (Intercept))

B
 (look
 in
 the
 row

Slope
  β
 (beta-­‐one)
  b
  labeled
 with
 the
 name

1 1
of
 the
 x-­‐variable)

Coefficient
 of
  Values
 in
 Correlation

  r

correlation
  Matrix

Coefficient
 of

  r2
  Multiple-­‐R
 Squared

determination

Error
 terms
 vs
  Unstandardized

ε(error
 terms)
  e
 (residuals)

Residuals
  residuals

5